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A294184 a(n) is the number of ways to arrange numbers from 1 to 2*n in a row, starting with 1, such that the sum of every two adjacent numbers is prime, but also considering the ends as adjacent. 0
1, 2, 2, 4, 96, 1024, 2880, 81024, 770144, 6309300, 213812336, 6395634044, 165849732426, 8050337724850, 255709623233382 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

When the size of the row is odd, it is impossible to find such an arrangement, so that sequence is only defined for even-sized rows.

LINKS

Table of n, a(n) for n=1..15.

Situ Zhengmei, Prime ring, Chinese Math Blog.

FORMULA

a(n) = 2*A051252(n), for n > 1. - Giovanni Resta, Feb 25 2020

EXAMPLE

a(1) = 1, because of [1, 2].

a(2) = 2, because of [1, 2, 3, 4] and [1, 4, 3, 2].

a(3) = 2, because of [1, 4, 3, 2, 5, 6] and [1, 6, 5, 2, 3, 4].

CROSSREFS

Cf. A036440, A051252, A051239, A242527, A242528.

Sequence in context: A067700 A270554 A037010 * A114695 A134084 A267346

Adjacent sequences: A294181 A294182 A294183 * A294185 A294186 A294187

KEYWORD

nonn,more

AUTHOR

Michel Marcus, Feb 11 2018

EXTENSIONS

a(9)-a(11) from Jackson Bahm, Feb 25 2020

a(12)-(15) from Giovanni Resta, using A051252, Feb 25 2020

STATUS

approved

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Last modified January 28 08:59 EST 2023. Contains 359850 sequences. (Running on oeis4.)